While the circuits were the unit of circuit riding assignments, the individual circuit courts were referred to by the name of the judicial district (e.g. "United States Circuit Court for the District of New Hampshire," or, in case citations, C.C.D.N.H.).

Some districts were not within any circuit (for example, under the Judiciary Act of 1801: Maine, Kentucky, and Tennessee). These district courts exercised the powers of circuit courts, and appeals from the district court were possible only to the Supreme Court. Circuit riding did not occur within such districts.